Cybernetics and Systems Analysis

, Volume 55, Issue 6, pp 905–913 | Cite as

Bilevel Optimization Problems of Distribution of Interbudgetary Transfers Under Given Limitations

  • I. V. SergienkoEmail author
  • N. V. Semenova
  • V. V. Semenov

The problems of optimal distribution of transfers within given budget limitations are formulated and analyzed. The mathematical model is presented as a bilevel linear optimization problem that contains linear problems of integer optimization at the lower level. Both optimistic and pessimistic versions of the problem are considered. For the approximate solution of optimistic version, the algorithm of finding local solutions for parametric lower-level integer programming problems on the basis of the method of directing neighborhoods is proposed. The auxiliary integer programming problem with Boolean variables of a higher level is solved based on local algorithms.


bilevel optimization problem, integer optimization parametric programming Boolean variables local algorithm 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. V. Mikhalevich and I.V. Sergienko, Modeling of Transition Economy: Models, Methods, Information Technologies [in Russian], Naukova Dumka, Kyiv (2005).Google Scholar
  2. 2.
    I. V. Sergienko and V.V. Semenov, “Modeling the system of intergovernmental transfers in Ukraine,” J. Autom. Inform. Sci., Vol. 45, Issue 8, 1–10 (2013).CrossRefGoogle Scholar
  3. 3.
    V. V. Semenov, “Modeling the influence of interbudgetary transfers of Ukraine on financing of social infrastructure,” Dopov. Nac. Akad. Nauk Ukr., No. 10, 47–53 (2013).Google Scholar
  4. 4.
    I. V. Sergienko, Topical Directions of Informatics. In memory of V.M. Glushkov, Springer, New York–Heidelberg–Dordrecht–London (2014).Google Scholar
  5. 5.
    V. V. Semenov, Economics and Statistical Models and Methods of the Analysis of Social Processes; Inequality, Poverty, Polarization, Vols. 1 and 2 [in Ukrainian], RVV PUSKU, Kyiv (2008).Google Scholar
  6. 6.
    I. V. Sergienko, Methods of Optimization and Systems Analysis for Problems of Transcomputational Complexity [in Ukrainian], Akademperiodyka, Kyiv (2010). 912Google Scholar
  7. 7.
    V. V. Semenov and N. V. Semenova, “Progressive redistribution in the system of interbudgetary transfers of Ukraine,” in: Teoriya Optym. Rishen’, V. M. Glushkov Inst. of Cybernetics, NAS of Ukraine (2014), pp. 68 75.Google Scholar
  8. 8.
    V. V. Semenov, Levelling Properties of the System of Interbudgetary Transfers of Ukraine (Spoleczno ekonomiczne problemy gospodarowania w warunkach transformacji [in Polish]), Warszawa (2011), pp. 117–131.Google Scholar
  9. 9.
    V. V. Semenov and N.V. Semenova, Progresiveness of Taxation Systems. Foreign Trade: Economics, Finance, Law, No. 2, 69–75 (2011).Google Scholar
  10. 10.
    I. V. Sergienko, Mathematical Models and Methods to Solve Discrete Optimization Problems [in Russian], Naukova Dumka, Kyiv (1988).Google Scholar
  11. 11.
    I. V. Sergienko, L. N. Kozeratskaya, and T. T. Lebedeva, Stability and Parametric Analyses of Discrete Optimization Problems [in Russian], Naukova Dumka, Kyiv (1995).Google Scholar
  12. 12.
    I. V. Sergienko and V. P. Shylo, Discrete Pptimization Problems: Issues, Methods, Solutions, Analysis [in Russian], Naukova Dumka, Kyiv (2003).Google Scholar
  13. 13.
    M. D. Mesarovic, D. Macko, and Y. Takahara, Theory of Hierarchical, Multilevel, Systems, Vol. 68, Elsevier Sci. (2000).Google Scholar
  14. 14.
    Yu. B. Germeyer, Games with Nonantagonistic Interests [in Russian], Nauka, Moscow (1976).Google Scholar
  15. 15.
    I. V. Beiko, P. M. Zin’ko, and O. G. Nakonechnyi, Problems, Methods, and Algorithms of Optimization [in Ukrainian], RVV NUVVP, Rivne (2011).Google Scholar
  16. 16.
    H. F. Stackelberg, Marktform und Gleichgewicht, Springer-Verlag, Berlin (1934).zbMATHGoogle Scholar
  17. 17.
    J. Bracken and J. T. McGill, “Mathematical programs with optimization problems in the constraints,” Operations Research, Vol. 21, No. 1, 37–44 (1973).MathSciNetCrossRefGoogle Scholar
  18. 18.
    O. Âen-Ayed, “Bilevel linear programming,” Comput. Oper. Res., Vol. 20, No. 5, 485–501 (1993).Google Scholar
  19. 19.
    J. Bard, Practical Bilevel Optimization.Algorithms and Applications. Kluwer Acad. Publ., Dordrecht (1998).CrossRefGoogle Scholar
  20. 20.
    S. Dempe, Foundations of Bilevel Programming, Kluwer Acad. Publ., Dordrecht (2002).zbMATHGoogle Scholar
  21. 21.
    L. N. Vicente and P. H. Calamai, “Bilevel and multilevel programming: A bibliography review,” J. Global Optim., Vol. 5, No. 3, 291–306 (1994).Google Scholar
  22. 22.
    S. Dempe, “Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints,” Optimization, Vol. 52, No. 3, 33–35 (2003).MathSciNetCrossRefGoogle Scholar
  23. 23.
    S. Dempe, Bilevel Programming. A Survey, Preprint TU Bergakademie Freiberg Nr. 2003-11, Fakultat fur Mathematik und Informatik.Google Scholar
  24. 24.
    P. Hansen, B. Jaumard, and G. Savard, “New branch-and-bound rules for linear bilevel programming,” SIAM. J. on Scientific and Statistical Computing, Vol. 13, 1194–1217 (1992).MathSciNetCrossRefGoogle Scholar
  25. 25.
    L. Vicente, G. Savard, and J. Judice, “Discrete linear bilevel programming problem,” J. of Optimization Theory and Applications, Vol. 89, No. 3, 597–614 (1996).MathSciNetCrossRefGoogle Scholar
  26. 26.
    A. Sinha, P. Malo, and K. Deb, “A review on bilevel optimization: From classical to evolutionary approaches and applications,” IEEE Trans. on Evolutionary Computation, Vol. 22, No. 2, 278–295 (2018).CrossRefGoogle Scholar
  27. 27.
    N. V. Semenova, “Methods of searching for guaranteeing and optimistic solutions to integer optimization problems under uncertainty,” Cybern. Syst. Analysis, Vol. 43, No. 1, 85–93 (2007).MathSciNetCrossRefGoogle Scholar
  28. 28.
    I. V. Sergienko and N. V. Semenova, “Integer programming problems with inexact data: Exact and approximate solutions,” Cybern. Syst. Analysis, Vol. 31, No. 6, 842–851 (1995).MathSciNetCrossRefGoogle Scholar
  29. 29.
    V. A. Roshchin, N. V. Semenova, and I. V. Sergienko, “Solution and investigation of one class of inexact integer programming problems,” Cybernetics, Vol. 25, No. 2, 185–193 (1989).MathSciNetCrossRefGoogle Scholar
  30. 30.
    N. V. Semenova, “Solution of a generalized integer-valued programming problem,” Cybernetics, Vol. 20, No. 5, 641–651 (1984).Google Scholar
  31. 31.
    J. F. Bard and J. Moore, “An algorithm for the discrete bilevel programming problem,” Naval Research Logistics, Vol. 39, 419–435 (1992).MathSciNetCrossRefGoogle Scholar
  32. 32.
    A. Caprara and M. Fischetti, “Odd cut-sets, odd cycles, and 0-1/2 Chvata–Gomory cuts Working Paper,” Univ. Padua.,Italy (1994).Google Scholar
  33. 33.
    L. N. Vicente, G. Savard, and J. J. Judice, “The discrete linear bilevel programming problem,” Report N. G-94–12, GERAD, Acole Polytechnique Universitѐ McGill, Montrѐal (1994).Google Scholar
  34. 34.
    I. V. Sergienko and V. P. Shylo, “Problems of discrete optimization: Challenges and main approaches to solve them,” Cybern. and Syst. Analysis, Vol. 42, No. 4, 465–482 (2006).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • I. V. Sergienko
    • 1
    Email author
  • N. V. Semenova
    • 1
  • V. V. Semenov
    • 1
  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

Personalised recommendations